If you take out an auto loan of $4,500 at 5% interest for 24 months (2 years), what will your monthly payment be?
Round your answer to the nearest cent.
To calculate the monthly payment for an auto loan, we can use the formula for calculating the monthly payment on a fixed-rate loan:
Monthly payment = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
P = Principal loan amount ($4,500 in this case)
r = Monthly interest rate (5% annual interest / 12 months)
n = Total number of payments (24 months)
Let's break down the calculation step by step:
Step 1: Convert the annual interest rate to a monthly interest rate.
Monthly interest rate = 5% / 100 / 12 = 0.05 / 12 = 0.00417
Step 2: Calculate the denominator of the monthly payment formula.
Denominator = (1 + r)^n - 1 = (1 + 0.00417)^24 - 1
Step 3: Calculate the numerator of the monthly payment formula.
Numerator = P * r * (1 + r)^n = $4,500 * 0.00417 * (1 + 0.00417)^24
Step 4: Calculate the monthly payment.
Monthly payment = Numerator / Denominator
Let's plug the values into the formula and calculate the monthly payment:
Denominator = (1 + 0.00417)^24 - 1 = 1.104984 - 1 = 0.104984
Numerator = $4,500 * 0.00417 * (1 + 0.00417)^24 ≈ $4,500 * 0.00417 * 1.104984 ≈ $20.623
Monthly payment = $20.623 / 0.104984 ≈ $196.08
So, the monthly payment for an auto loan of $4,500 at 5% interest for 24 months would be approximately $196.08 (rounded to the nearest cent).